This past winter I parked the wagon due to the battery getting weaker & needing new tires. I'd start it occasionally until the battery finally gave up. I had to recharge the battery to start it up, but it wouldn't hold a charge well enough. I bought the bigger battery & clamp, but then it wouldn't start.
It turns over & acts as if it wants to fire, but it never does. I see smoke coming from the exhaust which leads me to think its getting some fuel, but maybe not enough. I can hear a very faint hum from the in-tank pump, & that's with the seat bottoms up.
I pulled the fuel line from the filter & I get a little bit of fuel, but not much. It just dribbles from the line rather than squirting everywhere.
I've checked the air filter, installed a new fuel filter just in case, & I'm fairly sure the fuel is still good. Fuses are good & relays seem to be OK too.
Any thoughts?

When I turn the key, how much fuel should come from the line? I'm thinking the pump is at the point that it just can't give enough fuel to fire up even though it still hums just a little.

This past winter I parked the wagon due to the battery getting weaker & needing new tires. I'd start it occasionally until the battery finally gave up. I had to recharge the battery to start it up, but it wouldn't hold a charge well enough. I bought the bigger battery & clamp, but then it wouldn't start.
It turns over & acts as if it wants to fire, but it never does. I see smoke coming from the exhaust which leads me to think its getting some fuel, but maybe not enough. I can hear a very faint hum from the in-tank pump, & that's with the seat bottoms up.
I pulled the fuel line from the filter & I get a little bit of fuel, but not much. It just dribbles from the line rather than squirting everywhere.
I've checked the air filter, installed a new fuel filter just in case, & I'm fairly sure the fuel is still good. Fuses are good & relays seem to be OK too.
Any thoughts?

When I turn the key, how much fuel should come from the line? I'm thinking the pump is at the point that it just can't give enough fuel to fire up even though it still hums just a little.

your car has the pd fuel injection system, basically the lift pump sends fuel up to the injectors in excess, some is put into the cylider, the rest recirculates back to the tank

2004-2006 TDI (myturbodiesel.com)

These are all pumpe duse (PD), a new type of direct injection. It had been used in European TDI for a while before coming to North America. Check out the cosmetic differences between mk4 pumpe duse and non-pumpe duse Jetta to help identify what car you have (2004-2005 Passat TDI, BHW engine, and Touareg V10 TDI are all PD).
PD engines have significant mechanical differences from the earlier non-pumpe duse cars. 2004-2006 4th generation cars use the BEW engine (2004-2006 Golf/New Beetle) and 5th generation cars use the BRM engine (2005.5-2006 5th generation Jetta TDI). The difference is because the Jetta changed over to the 5th gen in 2005.5. All PD use a low pressure electric fuel pump (about 6-8 psi) in the fuel tank, something that earlier TDI did not. For a buying checklist for the early pumpe duse engines, see 1000q: pumpe duse engine checklist. For the A5 body pumpe duse, see 1000q: early A5 Jetta TDI buying checklist.

Gonna scan it after work with Vag-Com & already have the pump ready to go. I just wanna make sure that I've narrowed it to that first. It just seems odd that the last time it started, it fired right up & then 2 weeks later its not firing up. With the way the fuel just dribbles from the line, I'm almost sure its gonna be the pump. Plus I'm around 117K miles. Its probably due.

you could check battery voltage with starter engaged to see if you have voltage above the threshold for ecu operation, above 10.5. starter may have been damaged by operating with the weak/bad battery and may be drawing excessive amperage.

I hope that's not it, but it will be something I'll look into. I couldn't get to the wagon yesterday, so we'll see today if I can figure it out. I may just toss the new pump in & see if it works. I'd think that with the fuel line off the filter, it would spray fuel instead of just dribbling down the line when you cycle the key.